閤 Rules rather than Discretion: The Inconsistency of Optimal Plans OR。 Finn e Kydland; Edward C. Prescott The Journal of political Economy, Vol. 85, No. 3. (Jun, 1977), pp. 473-492 Stable url: http://inksistor.org/sici?sic0022-3808%028197706%02985%3a3%03c473%03arrtdt3e2.0.co%3b2-a The Journal of political Economy is currently published by The University of Chicago Press Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.htmlJstOr'sTermsandConditionsofUseprovidesinpartthatunlessyouhaveobtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the jsTOR archive only for your personal, non-commercial use Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.istor.org/iournals/ucpress.html Each copy of any part of a JSTOR transmission must contain the same copyright notice that ap on the screen or printed page of such transmission STOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support @jstor. org Fri Mar 161202:072007
Rules Rather than Discretion: The Inconsistency of Optimal Plans Finn E. Kydland; Edward C. Prescott The Journal of Political Economy, Vol. 85, No. 3. (Jun., 1977), pp. 473-492. Stable URL: http://links.jstor.org/sici?sici=0022-3808%28197706%2985%3A3%3C473%3ARRTDTI%3E2.0.CO%3B2-A The Journal of Political Economy is currently published by The University of Chicago Press. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/ucpress.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support@jstor.org. http://www.jstor.org Fri Mar 16 12:02:07 2007
Rules Rather than Discretion The Inconsistency of Optimal plans Finn E Kydland Norwegian School of Economics and Business Administration Edward C. Prescott Even if there is an agreed-upon, fixed social objective function and policymakers know the timing and magnitude of the effects of their ctions, discretionary policy, namely, the selection of that decision which is best, given the current situation and a correct evaluation of the end of-period position, does not result in the social objective function being maximized. The reason for this apparent paradox is that economic planning is not a game against nature but, rather a game against ational economic agents. We conclude that there is no way control theory can be made applicable to economic are rationa I. Introduction Optimal control theory is a powerful and useful technique for analyzing dynamic systems. At each point in time, the decision selected is best, given the current situation and given that decisions will be similarly selected in the future. Many have proposed its application to dynamic economic planning. The thesis of this essay is that it is not the appro- priate tool for economic planning even when there is a well-defined and agreed-upon, fixed social objective function. We find that a discretionary policy for which policymakers select the We would like to thank Walter Dolde, Leif Johansen, Robert E. Lucas, Jr, Christopher would like to acknowledge the support of the Guggenheim Foundation, National Science Foundation, and the Bank of norway
474 JOURNAL OF POLITICAL ECONOMY best action, given the current situation, will not typically result in the social objective function being maximized. Rather, by relying on some policy rules, economic performance can be improved. In effect this is an argument for rules rather than discretion, but, unlike Friedmans(1948 argument, it does not depend upon ignorance of the timing and magnitude of the effects of policy The reasons for this nonintuitive result are as follows: optimal control theory is an appropriate planning device for situations in which curren outcomes and the movement of the system,'s state depend only upon current and past policy decisions and upon the current state. But,we argue, this is unlikely to be the case for dynamic economic systems. Cur- rent decisions of economic agents depend in part upon their expectations of future policy actions. Only if these expectations were invariant to the future policy plan selected would optimal control theory be appropriate In situations in which the structure is well understood, agents will surely surmise the way policy will be selected in the future. Changes in the social objective function reflected in, say, a change of administration do have an immediate effect upon agents'expectations of future policies and affect their current decisions. This is inconsistent with the assump tions of optimal control theory, This is not to say that agents can fore cast future policies perfectly. All that is needed for our argument is that agents have some knowledge of how policymakers'decisions will change as a result of changing economic conditions. For example, agents may expect tax rates to be lowered in recessions and increased in booms The paradox also arises in situations in which the underlying economic structure is not well understood, which is surely now the case for aggre gate economic analyses, Standard practice is to estimate an econometric del and then, at least informally, to use optimal-control-theory techniques to determine policy. But as Lucas(1976) has argued, since optimal decision rules vary systematically with changes in the structure of series relevant to the decision maker, any change in policy will alt the structure of these rules, Thus cha policy induce changes in structure, which in turn necessitate reestimation and future changes in policy, and so on. We found for some not implausible structures that this iterative procedure does not converge, and, instead, stabilization efforts examples, however, it did converge, and the resulting policy was con- sistent but suboptimal. It was consistent in the sense that at each point in time the policy selected was best, given the current situation. In effect the policymaker is failing to take into account the effect of his policy rule upon the optimal decison rules of the economic agents In this paper, we first define consistent policy and explain for the is suboptimal. The implications of the analysis are then considered for patent policy and
RULES RATHER THAN DISCRETION 475 flood-control problems for which consistent policy procedures are not eriously considered. Then, for the aggregate demand management problem, it is shown that the application of optimal control theory is equally absurd, at least if expectations are rational. Doing what is best or price stability) were at the socially optimal rate. Consistency fo infinite-period recursive economic structures is then considered. In equili rium, optimizing agents follow rules which specify current decisions as a function of the current state 1 Methods are developed for computing these equilibrium decision rules for certain specialized structures.The methods are used to evaluate alternative investment-tax-credit policies designed both to stabilize and to yield optimal taxation. Among the policies evaluated is the suboptimal consistent policy. Within the class of feed back policy rules, we found that the optimal one depended upon the initial conditions. Thus it was not optimal to continue with the initial policy in subsequent periods; that is, the optimal policy was inconsistent. I. Consistent Policy Let I=(T1,T2,..., Tr)be a sequence of policies for periods (which may be infinite)and x =(*1, x2 r)be the corresponding sequence for economic agents'decisions. An agreed-upon social objective function is assumed to exist. 2 Further, agents'decisions in period\ depend. 7 S(a T) all policy decisions and their past decisions as follows xr=X(x1,…,x1-1,丌1,…,丌r),t=1 In such a framework an optimal policy, if it exists, is that feasible which maximizes(1) subject to constraints(2). The concept of consistency is less obvious and is defined as follows Definition: A policy r is consistent if, for each time period t, r maximizes(1), taking as given previous decisions, x I and that future policy decisions (s for s>t) are simila selected he original objective of this research was to demonstrate the applicability of consistent solution obtained by using control-theory techniques, but initially cons of our initial analyses, led us to the radical conclusions of this essay. 2 Uncertainty is not the central issue of this essay. As with Arrow- Debreu stat need only define the decision elements to be functions contingent upon observables to incorporate uncertainty as is done for the stabilization example in
The inconsistency of the optimal plan is easily demonstrated by a two-period example. For T= 2, I2 is selected so as to maximize (x1,x2,丌1,丌2), For a plan to be consistent, I, must maximize( 3), given the past decisions T1,*, and constraint (4). Assuming differentiability and an interior aS ax aS_0 The consi policy ignores the effects of decision rule, the first-order condition is CSax2SX1「 as aS aX2 ax2O2'aT2 aT2 Lax, ax2 ax, Only if either the effect of T2 upon x, is zero(i. e, aX,/aT,=0)or the effect of changes in x, upon S both directly and indirectly through xz is zero (ic, [aS/ax1 aS/ ax2 aX2/ax,]=0)would the consistent policy be optimal Pollak (1968)resolved a planning inconsistency which arose because different generations had different preference orderings by assuming at each stage that the policy selected was best (relative to that generation,s preferences), given the policies which will be followed in the future. For prol previous decisions T, and xu, is best ∏r( Once the functional relationship Ir is known, the determination of the 丌r-1=∏7-1(T1 T-2;x1 determined, and in general the consistent policy can be determined once future policy rules are known. With such a procedure, the policy decision at each stage is optimal, given the rules
RULES RATHER THAN DISCRETION 477 for future policy selection. But as the simple example illustrated, this procedure is suboptimal Two examples follow The issues are obvious in many well-known problems of public policy For example, suppose the socially desirable outcome is not to have houses built in a particular flood plain but, given that they are there to take certain costly fiood-control measures. If the government,s policy were not to build the dams and levees needed for flood protection and agents knew this was the case, even if houses were built there, rational agents would not live in the flood plains. But the rational agent knows that, if he and others build houses there, the government will take the necessary flood-control measures. Consequently, in the absence of a law prohibiting the construction of houses in the flood plain, houses are built there, and the army corps of engineers subsequently builds the dams and levees A second example is patent policy. Given that resources have been allocated to inventive activity which resulted in a new product or process, patent protection. For thi few would seriously consider this optimal-control-theory solution as being reasonable. Rather, the question would be posed in terms of the optimal patent life(see, e.g., Nordhaus 1969), which takes into consideration bot he incentive for inventive activity provided by patent protection and the loss in consumer surplus that results when someone realizes monopoly rents. In other words, economic theory is used to predict the effects of alternative policy rules, and one with good operating characteristics is selected Ill. The Inflation-Unemployment Example The suboptimality of the consistent policy is not generally recognized for the aggregate demand management problem, The standard policy prescription is to select that policy which is best, given the current situation.This may seem reasonable, but for the structure considered, which we argue is a plausible abstraction of realiti, in unemployment such policy results n excessive rates of inflation without any redi The policy of maintaining price stability is preferable There are some subtle game-theoretic issues which have not been addressed here. Peleg and Yaari ( 1973) criticized Pollak's solution because sometimes it did not exist and proposed an alternative solution to the noncooperative intergeneration game. As ex ined by K and(1975b), in the language of dynamic games, Pollak lution and Peleg and Yaari the open- loop solution For policy selection, the poli dominant, and for dominant-player games, the open-loop solution is inconsistent(sec Kydland 1975a, 1975b for further details ). That is why Peleg and Yaari's solution was not considered here
JOURNAL OF POLITICAL ECONOMY The attempts of economists to rationalize the apparent trade-off between unemployment and inflation in modern theoretical terms have resulted in models with the following structur ment)is a decreasing(increasing) function of the discrepancy between actual and expected inflation rates. This example assumes such a relation =A(x-x)+u*, where u, is unemployment in period t, i a positive constant, x, the in- fation rate, x f the forecasted or expected inflation rate, and u the natural rate implied by these theories, As has been recently shown by Phelps and Taylor(1975), one need not rely upon imperfect information across firms about the"generality"of shock or imperfect foresight abou the persistence of shock over time to obtain a similar relationship. They obtained one by assuming price rigidities, namely, that prices and wages are set prior to the realization of demand expectations. The conventional approach is to assume that expectations depend in some mechanical ad hoc way upon past prices. If so, control theory would be an appropriate tool to determine the optimal path of unemployment and inflation. The policy decision in each period would consider both current outcomes and a proper evaluation of the terminal price expectations state variable. Such a treatment of expectations is priori or amplI in administration which reflects a change in the relative costs society nd inflation will hay upon expectations--contrary to the implicit assumption of the proponer of control theory. Moreover, private agents or their agents have as much information about the economic structure as does the policymaker and some information concerning the implicit objective function which ration zes policy selections, Therefore their forecasts of future policy be havior will be related to actual policy selection. This does not imply that policy is perfectly predicted, but then neither is the behavior of private agents Just partial predictability of policy is sufficient to invalidate the use of optimal control theory For this example, we shall assume that the expectations are rational, so that the mathematical expectation of inflation equals the expected x Whether forecasts are rational is still open to debate. In Sargent (1973) the rational-expectations hypothesis is tested and accepted. He also explains why many other tests that rejected the hypothesis are invalid He does not, however, comment on the Hirsch and Lovell(1969)test
RULES RATHER THAN DISCRETION 479 consistent ibrium FIG 1.Consistent and optimal equilibrium errors were systematically related to lagged sales, so we will do so. c which used direct measures of expectations and found that foreca ses to this finding are that there may be biases in their measurement of expectations, and these biases are related to lagged sales. This is not implausible, given the subtleness of the expectations concept and the imprecision of survey instruments. Further, even if there were a system atic forecast error in the past, now that the Hirsch and Lovell results are part of agents' information sets, future forecast errors should not be subject to such biases. To complete the model, a theory of policy selection is needed. Here it is assumed that there is some social objective function which rationalizes S(xr, ut) If the rationalization is not perfect, a random term must be introduced into the function, The consistent policy maximizes this function subject to the Phillips curve constraint (5) Figure I depicts some Phillips curves and indifference curves From(5) the Phillips curves are straight lines having slope -2-I and intersecting the vertical axis at xr. For a consistent equilibrium, the indifference curve must be tangent to a Phillips curve at a point along the vertical axis as at point C. Only then are expectations rational and the policy selected
JOURNAL OF POLITICAL ECONOMY t,given the current situation. The indifference curves imply that the socially preferred inflation rate is zero, which seems consistent with the publics preferences. We of course recognize that inflation is a tax on reserves and currency, and a more informed public might prefer some positive or negative inflation rate. If so, x need only be interpreted as deviation from the optimal rate. The outcome of a consistent policy selection clearly is not optimal. If the policymakers were compelled to maintain price stability and did not have discretionary powers, the re- sulting equilibrium would have no higher unemployment than the con sistent policy. The optimal equilibrium is point O, which lies on a highe indifference curve than the consistent-equilibrium point C t is perhaps worthwhile to relate our analysis to that of Taylors (1975), in which he found that the optimal monetary policy was random in a rational-expectations world. Similar results would hold for our prob- lem if uncertainty in the social objective function had been introduced Both for his structure and for ours, the optimal policy is inconsistent, and consequently it is not optimal for the policymaker to continue with his original policy rules IV. Consistent Planning for the Infinite Horizon The method of backward induction cannot be applied to infinite-period problems to determine a consistent policy because, unlike the finite period problem, there is no final period with which to begin the induc tion. For recursive structures, however, the concept of consistency be defined in terms of policy rules. Suppose that the economy at time t can be described by a vector of state variables yr, a vector of policy variables Tr, a vector of decision variables x, for the economic agents and a vector of random shocks e, which are temporally independent The movernent over time of these variables is given by the system of y+1=F(y1,r;x2E1 Let the feedback policy rule for future periods be For certain structures, rational economic agents will in the future follow a rule of the form d(ys;∏ It te that changes in policy rule ni change the func tional form of d a point convincingly made by Lucas(1976)in his critique of current econometric policy-evaluation procedures. The decisions of agents in the current period will have the form d(y2r;∏)
RULES RATHER THAN DISCRETION Again, it is important to note that expectations of future policy affect current decisions. For example, the effect of an increase in the inves ment tax credit will depend upon the expected future level investment tax credit If, in addition, the social objective function is of the form ∑R(xny,兀,0<Bn and the objective is to minimize its expected value, the optimal value for T, will depend upon both y, and nl the policy rule which will be used in the future. In other words, the best policy rule for the current period nI(y) is functionally related to the policy rule used in the future ∏(y),say ∏=g(∏) A stationary policy rule II is consistent if it is a fixed point of mapping g, for then it is best to use the same policy rule as the one expected to b used in the future. 4 Suppose policymakers and agents do not have a clear understanding of the dynamic structure of the economy. Over time, agents will grope for and most likely converge to the equilibrium rules of forms(6)and olicymakers taking the decision rules of agents as given, when evaluating alternative decisions, typically would consider the trade-off of current outcomes relative to the desirability or value of the end-of- period state. Assuming that their valuation of the terminal state is oximately correct, they will be selecting the approximately consistent policy, assuming also that agents have approximately rational expect tions. Thus it seems likely that the current practice of selecting that policy hich is best, given the current situation, is likely to converge to the consistent but suboptimal policy. 5 It is hard to fault a policymaker acting consistently. The reason that such policies are suboptimal is not due to myopia. The effect of this decision upon the entire future is taken into consideration. Rather, the suboptimality arises because there is no mechanism to induce future policymakers to take into consideration the effect of their policy, via the expectations mechanism, upon current decisions of agents This is the solution concept used by Phelps and Pollak(1968)for an infinite-period ccond-best growth problem when different generations had inconsistent preferences policies. Within the class of linear feedback rules n(n), we found that the best pol,t rule depended upon the initial condition. The most general class of decision polici re characterized by a sequence of probability measures indexed by the history r,y)), with the superscripted variables denot of the variables. It was necessary to consider probability distributions because for some games a randomized strategy will be optimal and not dominated by a deterministic one, For games against nature, only deterministic strategies need be considered
